The B. Searcy double rifles made today have a double under bolt (PURDEY type) The actions are not A&D but are made from scratch, by Butch, from Barstock stainless of very tough number, and do not need a third bite. his actions are sized to the cartridge they are chambered to.
His first doubles, made years ago, (early1980s) were converted Browning BSS actions, fitted with a third lock-up in the form of a rib extention. The actions were re-heat treated after the fitting was done, and there is one example of these that had over 3000 rounds of 470NE shot through it before it was sold to a PH in Africa, where it is still poping Buffalo, as far as I know!
The third lock-up is probably not needed on most modern double rifles today, and in any event, are only back-up safeties.
The double rifles one sees, that are off face, were more likely to have been put off face by poor care in the hook, and pin area, letting wear of these mateing surfaces loosen the fit, not because of the lack of a third bite, doll's head, or hidden extention.
I'd say if you want a Searcy don't pass it because of the lack of a third fastener, because with normal care, and use of proper pressured ammo, you will never shoot a 577NE enough in your life time to take his rifle off face! IMO, it is a non-issue!